THE COMPLETE GRAVITY GRADIENT TENSOR DERIVED FROM THE VERTICAL COMPONENT OF GRAVITY: A FOURIER TRANSFORM TECHNIQUE

Abstract

A technique has been to developed to determine the complete gravity gradient tensor from pre-existing vertical gravity data using the fast Fourier Transform (FFT). Since direct measurement of the entire gravity gradient tensor is generally unavailable, our technique provides an alternative determination of the gravity gradient tensor components. Traditionally, derivatives of vertical gravity (gz,x, gz,y, and gz,z) have been the only gravity gradient tensor components that have been computed directly. Gravity gradient tensor components are computed for four different, three-dimensional (3-D), idealized horst-and-graben models, with varying depths to the horst. Comparing the FFT results with calculated gradient components from the 3-D models shows that the RMS error for each component, between the two results, is at most ~3.3 Eotvos Units. In addition, measured gravity gradient components from an airborne survey over the Wichita Uplift and Anadarko Basin region of southwest Oklahoma compare favorably with the FFT-derived results using available vertical gravity data. No error analysis was attempted between the two results due to a low signal-to-noise ratio in the measured data. Our technique offers a novel way to transform and visualize the available data, and it also offers an inexpensive and previously unavailable subsurface mapping capability.